The week between Christmas and New Year's Day is the busiest week of the year, reliably busier than the 4th of July week. It is so much busier that Disney actually created annual passes for locals that specifically block them out from visiting during that hectic time (but which are still valid all summer including July 4).
Historically, the parks are all packed during Christmas week, and others on this board can share their stories about phased closures at the Magic Kingdom during that time. While many guests truly enjoy the magic and energy found at Disney World during Christmas week, if you do not enjoy extremely crowded conditions, you would be right to be afraid. Be very afraid.